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  • 泛函分析(英文版·原书第2版·典藏版) (美)沃尔特·鲁丁(Walter Rudin) 著 大中专 文轩网
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    • 作者: (美)沃尔特·鲁丁(Walter Rudin)著
    • 出版社: 机械工业出版社
    • 出版时间:2020-05-01 00:00:00
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    • 作者: (美)沃尔特·鲁丁(Walter Rudin)著
    • 出版社:机械工业出版社
    • 出版时间:2020-05-01 00:00:00
    • 版次:1
    • 印次:1
    • 印刷时间:2020-05-01
    • 页数:424
    • 开本:16开
    • 装帧:平装
    • ISBN:9787111654742
    • 国别/地区:中国
    • 版权提供:机械工业出版社

    泛函分析(英文版·原书第2版·典藏版)

    作  者:(美)沃尔特·鲁丁(Walter Rudin) 著
    定  价:99
    出 版 社:机械工业出版社
    出版日期:2020年05月01日
    页  数:424
    装  帧:平装
    ISBN:9787111654742
    主编推荐

    内容简介

    本书是国际有名教材,在材料的取舍和处理手法上很有特色,对某些公理进行了准确描述,并精彩地讨论了一些深入的专题,还介绍了在其他数学分支(如微分方程)中有价值的应用。用作者自己的话来讲,他并不期望写一部百科全书,而是为进一步的探索打开通道。本书叙述清楚,论证严谨,不少地方的注释相当精辟并具有启发性,可作为高等院校数学专业高年级本科生和研究生的教材和参考书。

    作者简介

    精彩内容

    目录
    Preface
    About the Author
    Part I General Theory
    1 Topological Vector Spaces
    Introduction
    Separation properties
    Linear mappings
    Finite-dimensional spaces
    Metrization
    Boundedness and continuity
    Seminorms and local convexity
    Quotient spaces
    Examples
    Exercises
    2 Completeness
    Baire category
    The Banach-Steinhaus theorem
    The open mapping theorem
    The closed graph theorem
    Bilinear mappings
    Exercises
    3 Convexity
    The Hahn-Banach theorems
    Weak topologies
    Compact convex sets
    Vector-valued integration
    Holomorphic functions
    Exercises
    4 Duality in Banach Spaces
    The normed dual of a normed space
    Adjoints
    Compact operators
    Exercises
    5 Some Applications
    A continuity theorem
    Closed subspaces of Lp-spaces
    The range of a vector-valued measure
    A generalized Stone-Weierstrass theorem
    Two interpolation theorems
    Kakutani's fixed point theorem
    Haar measure on compact groups
    Uncomplemented subspaces
    Sums of Poisson kernels
    Two more fixed point theorems
    Exercises
    Part Ⅱ Distributions and Fourier Transforms
    6 Test Functions and Distributions
    Introduction
    Test function spaces
    Calculus with distributions
    Localization
    Supports of distributions
    Distributions as derivatives
    Convolutions
    Exercises
    7 Fourier Transforms
    Basic properties
    Tempered distributions
    Paley-Wiener theorems
    Sobolev's lemma
    Exercises
    8 Applications to Differential Equations
    Fundamental solutions
    Elliptic equations
    Exercises
    9 Tauberian Theory
    Wiener's theorem
    The prime number theorem
    The renewal equation
    Exercises
    Part Ⅲ Banach Algebras and Spectral Theory
    10 Banach Algebras
    Introduction
    Complex homomorphisms
    Basic properties of spectra
    Symbolic calculus
    The group of invertible elements
    Lomonosov's invariant subspace theorem
    Exercises
    11 Commutative Banach Algebras
    Ideals and homomorphisms
    Gelfand transforms
    Involutions
    Applications to noncommutative algebras
    Positive functionals
    Exercises
    12 Bounded Operators on a Hilbert Space
    Basic facts
    Bounded operators
    A commutativity theorem
    Resolutions of the identity
    The spectral theorem
    Eigenvalues of normal operators
    Positive operators and square roots
    The group of invertible operators
    A characterization of B*-algebras
    An ergodic theorem
    Exercises
    13 Unbounded Operators
    Introduction
    Graphs and symmetric operators
    The Cayley transform
    Resolutions of the identity
    The spectral theorem
    Semigroups of operators
    Exercises
    Appendix A Compactness and Continuity
    Appendix B Notes and Comments
    Bibliography
    List of Special Symbols
    Index

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